chore: improve prettier lint

[brojd]

Closes #582

• Changed all lint:prettier scripts from prettier 'src/**/*.ts' --check to prettier . --check so .tsx, .json,
  .md, and config files are covered
• Fixed convai-widget-embed which was missing the --check flag
• Added lint:prettier to @elevenlabs/types (previously had none)
• Added format script (prettier . --write) to all packages and a pnpm format root command via turbo
• Added .prettierignore files per package to exclude dist/, generated files, and worklets. This was needed because prettier doesn't respect root .gitignore when running inside pnpm workspaces
• Ran pnpm format to apply prettier changes across all affected packages to fix existing formatting

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Note

Medium Risk
Mostly formatting/tooling changes, but it rewrites a large generated types file and updates Prettier inputs/ignores across packages, which could cause noisy diffs or missed/extra files in CI if misconfigured.

Overview
Improves Prettier linting and formatting across the monorepo. lint:prettier is standardized to run prettier . --check (covering TSX/JSON/MD/configs) and a new format script (prettier . --write) is added in packages plus root-level pnpm format/pnpm lint:prettier via Turborepo.

Adds per-package .prettierignore files to exclude dist/ and generated/worklet outputs, and updates turbo.json so lint:prettier considers all files plus .prettierignore while format runs uncached. The PR also applies Prettier-driven formatting to docs/config/tests and regenerates/reformats packages/types/generated/types/asyncapi-types.ts.

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[kraenhansen]

To reduce the amount of conflicts, I'd like for this to merge after we're merged next into main.

[brojd]

Sound good @kraenhansen 👍 I can solve the conflicts after the next -> main merge. That will be easy because we can just revert d001bd6 and rerun pnpm format against codebase after merge